She's famous, no doubt, but it hasn't gone to her head. And while she's traveled the world with her boyfriend Ben Hanisch (a total disaster, by the way), the Snatched star doesn't pretend her love life is any more glamorous than it really is. Case in point: "I went down on Ben this morning and he yawned. It was an accident, but we were both just dying laughing," the comic says in British Glamour's May issue (on stands Apr. 30) "I'm happy, but obviously I was like, 'F--k you!'"

"When I'm down there, if it's more than a minute, it's his birthday or something," she jokes. "But this morning it just happened—and then he yawned and it was a great excuse to stop."

Hanisch, who relocated from Chicago to live with Schumer in New York City, has been an ideal boyfriend so far. "He's very protective of me," she says. "Like, not overprotective, but if someone's taking pictures of me or filming in a restaurant, he'll start taking pictures of them."

"He's really cool; it's not a problem to be around any of the sorts of people who are at these events. He takes it all in his stride," she adds. "But when I say, 'Shall we get out of here?,' he's like, 'Yes!' I'm so lucky that I met him. And he hadn't seen any of my work before we met…"

Hanisch might be the only person who hadn't.

Michael Kovac/Getty Images for Moet & Chandon

Schumer has been on the rise for years. After working the stand-up circuit, she found success with Comedy Central's Inside Amy Schumer. A hit movie and a best-selling book followed, but Schumer—whose family lost nearly everything during the recession—says she's never been motivated by fame or money. "No, I did not ever want to be famous, honestly. It didn't occur to me until it was already happening. The fame aspect is not something that appealed to me at all. And I was really kind of terrified of it," Schumer tells the magazine. "I wouldn't trade it to wait tables or whatever. I live my life; I'm grateful for everything. It's mostly just really annoying."

Being famous is more "distracting" and "embarrassing for everyone" than anything else, she says. "I'm conscious for the people I'm with. Now when I go outside, I get photographed by the paparazzi." It could be worse, of course. "I'm not to the level of some people some actresses where it's constant tabloids," Schumer explains, "but it's enough that it's really uncomfortable."

To stay sane, Schumer keeps her eye on the prize. She's already worked with everyone from John Cena to Bill Hader, and there are "so many" more men she wants to kiss onscreen. (Sorry, Hanisch—British Glamour had to ask!) She wouldn't kick Tom Hardy "out of bed," nor would pass up Christian Bale or Idris Elba. "I mean, this is just a list of who I wanna sleep with, right?"